URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=JBM075&collegejaar=2025&taal=enDescription
Systems of linear equations are often used in economics and business. For this reason a course is included that concentrates on this topic: Linear Algebra. One of the methods discussed in this course is a method to decide whether a system of equations has none, one or multiple solutions. With this method the solution set itself can be determined and furthermore it gives insight in its geometric structure. For the special case that the number of equations equals the number of variables, a simple criterion can be deduced to check whether the system has precisely one solution. This criterion can also be used to actually calculate this unique solution. Furthermore, in this course several tools are introduced that will be used in other courses of the program.Content:
Systems of linear equations, Gaussian elimination, matrices, vectors, span, linear independence, linear transformations, inverses, determinants, vector spaces, subspaces, basis, dimension, rank, orthogonality, projections, eigenvalues, quadratic forms, definiteness.
Objectives
To give insight in the algebraic and geometric structure of vector spaces and solution sets of linear systems. Upon successful completion of the course, students are able to:
· Explain and compare the four methods Elementary Row Reducing, Inverse, and Matrix Factorization to solve a set of linear equations;
· Choose and apply an appropriate method to solve a set of linear systems originating from optimization, dynamical systems, statistics and econometrics;
· Apply different techniques in linear algebra to compute linear transformations, the determinant and inverse of a matrix;
· Explain the concepts of vector spaces and subspaces, detect whether a set vectors are linearly dependent and compute the corresponding basis;
· Illustrate the relationship between different concepts of linear algebra that are needed in optimization by applying mathematical reasoning;
· Prove theorems in Linear Algebra using for instance proof by contradiction or proof by construction;
· Model the relationship between different variables using Least Squares Optimization.